n. a polynomial equation in several unknowns, with integral coefficients, to be solved or proved insoluble in integers, such as Pythagoras' theorem or Fermat's last theorem. In 1970, Matiyasevich proved that no general algorithm exists for determining whether a given Diophantine equation is soluble, thereby answering Hilbert's tenth problem. (Named after the 3rd century BC Greek mathematician, Diophantus of Alexandria, of whose life all that is known are the ages of his marriage and death, inferred from an arithmetic riddle. Only six of the supposed 13 books of his Arithmetica are extant, but these introduced the earliest known algebraic notation, and deal with the algebraic solution, in the rationals, of a wide range of number theoretic and geometric problems.)